V. V. Ostapenko, “On the strong monotonicity of the CABARET scheme”, Zh. Vychisl. Mat. Mat. Fiz., 52:3 (2012), 447–460; Comput. Math. Math. Phys., 52:3 (2012), 387

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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2012, Volume 52, Number 3, Pages 447–460 (Mi zvmmf9669)

This article is cited in 24 scientific papers (total in 24 papers)

On the strong monotonicity of the CABARET scheme

V. V. Ostapenko

Lavrent’ev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, pr. Akademika Lavrent’eva 15, Novosibirsk, 630090 Russia

Full-text PDF (612 kB) Citations (24)

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Abstract: The strong monotonicity of the CABARET scheme with single flux correction is analyzed as applied to the linear advection equation. It is shown that the scheme is strongly monotone (has the NED property) at Courant numbers

r \in (0, 0.5]

$r\in (0,0.5]$ , for which it is monotone. Test computations illustrating this property of the CABARET scheme are presented.

Key words: CABARET finite difference scheme, strong monotonicity, flux corrected transport.

Received: 02.09.2011

English version:
Computational Mathematics and Mathematical Physics, 2012, Volume 52, Issue 3, Pages 387–399
DOI: https://doi.org/10.1134/S0965542512030141

Bibliographic databases:

Document Type: Article

UDC: 519.63

Language: Russian

Citation: V. V. Ostapenko, “On the strong monotonicity of the CABARET scheme”, Zh. Vychisl. Mat. Mat. Fiz., 52:3 (2012), 447–460; Comput. Math. Math. Phys., 52:3 (2012), 387–399

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Linking options:

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This publication is cited in the following 24 articles:

Alexander Sukhinov, Alexander Chistyakov, Inna Kuznetsova, Yulia Belova, Elena Rahimbaeva, “Development and Research of a Modified Upwind Leapfrog Scheme for Solving Transport Problems”, Mathematics, 10:19 (2022), 3564
Kulikov Yu.M. Son E.E., “Double Shear Layer Evolution on the Non-Uniform Computational Mesh”, Phys. Scr., 96:12 (2021), 125262
V. V. Ostapenko, T. V. Protopopova, “On monotonicity of CABARET scheme approximating the multidimensional scalar conservation law”, Num. Anal. Appl., 13:4 (2020), 360–367
Yu. M. Kulikov, E. E. Son, “Taylor-green vortex simulation using CABARET scheme in a weakly compressible formulation”, Eur. Phys. J. E, 41:3 (2018), 41
N. A. Zyuzina, V. V. Ostapenko, E. I. Polunina, “Splitting method for CABARET scheme approximating the non-uniform scalar conservation law”, Num. Anal. Appl., 11:2 (2018), 146–157
V. V. Ostapenko, “On strong monotonicity of two-layer in time CABARET scheme”, Math. Models Comput. Simul., 11:1 (2019), 1–8
N. A. Zyuzina, O. A. Kovyrkina, V. V. Ostapenko, “On the monotonicity of the CABARET scheme approximating a scalar conservation law with alternating characteristic field”, Math. Models Comput. Simul., 11:1 (2019), 46–60
N. A. Zyuzina, V. V. Ostapenko, “Decay of unstable strong discontinuities in the case of a convex-flux scalar conservation law approximated by the CABARET scheme”, Comput. Math. Math. Phys., 58:6 (2018), 950–966
O. A. Kovyrkina, V. V. Ostapenko, “Monotonicity of the CABARET scheme approximating a hyperbolic system of conservation laws”, Comput. Math. Math. Phys., 58:9 (2018), 1435–1450
V. V. Ostapenko, O. A. Kovyrkina, “Wave flows induced by lifting of a rectangular beam partly immersed in shallow water”, J. Fluid Mech., 816 (2017), 442–467
M. A. Zaitsev, S. A. Karabasov, “Skhema Kabare dlya chislennogo resheniya zadach deformirovaniya uprugoplasticheskikh tel”, Matem. modelirovanie, 29:11 (2017), 53–70
V. V. Ostapenko, A. A. Cherevko, “Application of the CABARET scheme for calculation of discontinuous solutions of the scalar conservation law with nonconvex flux”, Dokl. Phys., 62:10 (2017), 470–474
O. A. Kovyrkina, V. V. Ostapenko, “Monotonicity of the CABARET scheme approximating a hyperbolic equation with a sign-changing characteristic field”, Comput. Math. Math. Phys., 56:5 (2016), 783–801
O. Kovyrkina, V. Ostapenko, “On the monotonicity of multidimensional finite difference schemes”, Application of Mathematics in Technical and Natural Sciences, 8th International Conference for Promoting the Application of Mathematics in Technical and Natural Sciences - AMiTaNS-16 (Albena, Bulgaria, 22–27 June 2016), AIP Conf. Proc., 1773, ed. M. Todorov, Amer. Inst. Phys., 2016, 100007
A. A. Cherevko, T. S. Gologush, V. V. Ostapenko, I. A. Petrenko, A. P. Chupakhin, “Modeling process of embolization arteriovenous malformation on the basis of two-phase filtration model”, All-Russian Conference on Nonlinear Waves: Theory and New Applications (Wave16), Journal of Physics Conference Series, 722, IOP Publishing Ltd, 2016, UNSP 012009
M F Ivanov, A D Kiverin, S G Pinevich, I S Yakovenko, “Application of dissipation-free numerical method CABARET for solving gasdynamics of combustion and detonation”, J. Phys.: Conf. Ser., 754:10 (2016), 102003
N. A. Zyuzina, V. V. Ostapenko, “On the monotonicity of the cabaret scheme approximating a scalar conservation law with a convex flux”, Dokl. Math., 93:1 (2016), 69–73
N. A. Zyuzina, V. V. Ostapenko, “Monotone approximation of a scalar conservation law based on the CABARET scheme in the case of a sign-changing characteristic field”, Dokl. Math., 94:2 (2016), 538–542
V. V. Kuznetsova, V. V. Ostapenko, “Flows caused by rise of a rectangular bar partially immersed in shallow water”, Dokl. Phys., 61:3 (2016), 133–137
N. A. Zyuzina, V. V. Ostapenko, “Modification of the Cabaret scheme ensuring its high accuracy on local extrema”, Math. Models Comput. Simul., 8:3 (2016), 231–237

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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